Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.  Specifically, the models consider multivariate Ornstein-Uhlenbeck processes in equilibrium.  This leads to Gaussian models in which the covariance matrix is determined by the continuous Lyapunov equation.  In this setting, each graphical model assumes a sparse drift matrix with support determined by a directed graph.  The talk will discuss identifiability of such sparse drift matrices as well as their regularized estimation.